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Simplifying 0 = h2 + 10h + -36 Reorder the terms: 0 = -36 + 10h + h2 Solving 0 = -36 + 10h + h2 Solving for variable 'h'. Combine like terms: 0 + 36 = 36 36 + -10h + -1h2 = -36 + 10h + h2 + 36 + -10h + -1h2 Reorder the terms: 36 + -10h + -1h2 = -36 + 36 + 10h + -10h + h2 + -1h2 Combine like terms: -36 + 36 = 0 36 + -10h + -1h2 = 0 + 10h + -10h + h2 + -1h2 36 + -10h + -1h2 = 10h + -10h + h2 + -1h2 Combine like terms: 10h + -10h = 0 36 + -10h + -1h2 = 0 + h2 + -1h2 36 + -10h + -1h2 = h2 + -1h2 Combine like terms: h2 + -1h2 = 0 36 + -10h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 10h + h2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 10h + 36 + h2 = 0 + 36 Reorder the terms: -36 + 36 + 10h + h2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 10h + h2 = 0 + 36 10h + h2 = 0 + 36 Combine like terms: 0 + 36 = 36 10h + h2 = 36 The h term is 10h. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10h + 25 + h2 = 36 + 25 Reorder the terms: 25 + 10h + h2 = 36 + 25 Combine like terms: 36 + 25 = 61 25 + 10h + h2 = 61 Factor a perfect square on the left side: (h + 5)(h + 5) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (h + 5) equal to 7.810249676 and -7.810249676.Subproblem 1
h + 5 = 7.810249676 Simplifying h + 5 = 7.810249676 Reorder the terms: 5 + h = 7.810249676 Solving 5 + h = 7.810249676 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = 7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + h = 7.810249676 + -5 h = 7.810249676 + -5 Combine like terms: 7.810249676 + -5 = 2.810249676 h = 2.810249676 Simplifying h = 2.810249676Subproblem 2
h + 5 = -7.810249676 Simplifying h + 5 = -7.810249676 Reorder the terms: 5 + h = -7.810249676 Solving 5 + h = -7.810249676 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = -7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + h = -7.810249676 + -5 h = -7.810249676 + -5 Combine like terms: -7.810249676 + -5 = -12.810249676 h = -12.810249676 Simplifying h = -12.810249676Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.810249676, -12.810249676}
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